Bethe–Salpeter equation spectra for very large systems

Abstract

We present a highly efficient method for the extraction of optical properties of very large molecules via the Bethe-Salpeter equation. The crutch of this approach is the calculation of the action of the effective Coulombic interaction, $W$, through a stochastic TD Hartree propagation, which uses only 10 stochastic orbitals rather than propagating the full sea of occupied states. This leads to a scaling that is at most cubic in system size, with trivial parallelization of the calculation. We apply this new method to calculate the spectra and electronic density of the dominant excitons of a carbon-nanohoop bound fullerene system with 520 electrons, using less than 4000 core hours.

Deterministic/Fragmented-Stochastic Exchange for Large-Scale Hybrid DFT Calculations

“…It will be useful both for real-time TDDFT and for frequencyresolved TDDFT and BSE. 36,37 We also expect applications within atomic orbital basis set-based DFT codes, where the wave function is eventually represented on a complete grid. Additionally, we anticipate that this method will have applications in auxiliary field quantum Monte Carlo methods, where the bulk of the computational effort also lies in evaluating exchange energy on many Slater determinants.…”

“…Our formalism will also apply to time-dependent hybrid-DFT, where, like in GKS–DFT SCF, the ⟨ϕ q ϕ s |ξ⟩ vectors would be evaluated once while the exchange matrix, eqs and , will be updated repeatedly, here once per time step. It will be useful both for real-time TDDFT and for frequency-resolved TDDFT and BSE. , We also expect applications within atomic orbital basis set-based DFT codes, where the wave function is eventually represented on a complete grid. Additionally, we anticipate that this method will have applications in auxiliary field quantum Monte Carlo methods, where the bulk of the computational effort also lies in evaluating exchange energy on many Slater determinants. − …”

Excitons in organic materials: revisiting old concepts with new insights

“…This method was successfully applied to crystalline semiconductors and insulators for decades providing excellent agreement with experimental results [53]. GW/BSE calculations have recently established themselves also in the context of isolated molecules and clusters providing a good alternative to hybrid TDDFT [54][55][56][57][58][59][60]. Their added value is to offer, in addition to optical spectra, quantitative information about binding energies and spatial distribution of the excitations.…”

Connecting the Dots for Fundamental Understanding of Structure-Photophysics-Property Relationships of COFs, MOFs, and Perovskites using a Multiparticle Holstein Formalism

“…Despite significant recent progress, two main challenges still persist which involve a quantitative understanding of how electron-phonon coupling and defects influence the electronic, optical, and transport properties of functional electronic materials. Although, excited state properties of materials can be modeled using linear-response time-dependent density functional theory (LR-TDDFT) or the Bethe-Salpeter equation (BSE), 164 the presence of a large number of atoms in 2D materials makes the application of LR-TDDF and BSE computationally very demanding (however, recent advances look very promising 165,166 ). Moreover, electron-phonon coupling and different forms of electronic and conformational defects play fundamental roles in determining the photophysical response and, consequently, the transport properties of most organic and hybrid materials.…”